/// @file
/// @author David Pilger <dpilger26@gmail.com>
/// [GitHub Repository](https://github.com/dpilger26/NumCpp)
///
/// License
/// Copyright 2018-2021 David Pilger
///
/// Permission is hereby granted, free of charge, to any person obtaining a copy of this
/// software and associated documentation files(the "Software"), to deal in the Software
/// without restriction, including without limitation the rights to use, copy, modify,
/// merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
/// permit persons to whom the Software is furnished to do so, subject to the following
/// conditions :
///
/// The above copyright notice and this permission notice shall be included in all copies
/// or substantial portions of the Software.
///
/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
/// INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
/// PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE
/// FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
/// OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
/// DEALINGS IN THE SOFTWARE.
///
/// Description
/// Special Functions
///
#pragma once

#if defined(__cpp_lib_math_special_functions) || !defined(NUMCPP_NO_USE_BOOST)

#include "NumCpp/Core/Internal/Error.hpp"
#include "NumCpp/Core/Internal/StaticAsserts.hpp"
#include "NumCpp/Core/Internal/StlAlgorithms.hpp"
#include "NumCpp/NdArray.hpp"

#ifdef __cpp_lib_math_special_functions
#include <cmath>
#else
#include "boost/math/special_functions/ellint_3.hpp"
#endif

#include <type_traits>

namespace nc
{
    namespace special
    {
        //============================================================================
        // Method Description:
        /// Computes the incomplete elliptic integral of the second kind of k, v, and p.
        /// NOTE: Use of this function requires either using the Boost
        /// includes or a C++17 compliant compiler.
        ///
        /// @param      inK: elliptic modulus or eccentricity
        /// @param      inV: elliptic characteristic
        /// @param      inP: Jacobi amplitude (measured in radians)
        /// @return
        ///				calculated-result-type 
        ///
        template<typename dtype1, typename dtype2, typename dtype3>
        auto ellint_3(dtype1 inK, dtype2 inV, dtype3 inP)
        {
            STATIC_ASSERT_ARITHMETIC(dtype1);
            STATIC_ASSERT_ARITHMETIC(dtype2);
            STATIC_ASSERT_ARITHMETIC(dtype3);

#ifdef __cpp_lib_math_special_functions
            return std::ellint_3(inK, inV, inP);
#else
            return boost::math::ellint_3(inK, inV, inP);
#endif
        }

        //============================================================================
        // Method Description:
        /// Computes the incomplete elliptic integral of the second kind of k, v, and p.
        /// NOTE: Use of this function requires either using the Boost
        /// includes or a C++17 compliant compiler.
        ///
        /// @param      inArrayK: the order of the bessel function
        /// @param      inArrayV: elliptic characteristic
        /// @param      inArrayP: Jacobi amplitude (measured in radians)
        /// @return
        ///				NdArray
        ///
        template<typename dtype1, typename dtype2, typename dtype3>
        auto ellint_3(const NdArray<dtype1>& inArrayK, const NdArray<dtype2>& inArrayV, const NdArray<dtype3>& inArrayP)
        {
            if (inArrayK.size() != inArrayV.size() || 
                inArrayK.size() != inArrayP.size())
            {
                THROW_INVALID_ARGUMENT_ERROR("Shapes of inArrayK, inArrayV, and inArrayP must match.");
            }

            NdArray<decltype(ellint_3(dtype1{ 0 }, dtype2{ 0 }, dtype3{ 0 }))> returnArray(inArrayK.shape());

            for (uint32 i = 0; i < inArrayK.size(); ++i)
            {
                returnArray[i] = ellint_3(inArrayK[i], inArrayV[i], inArrayP[i]);
            }

            return returnArray;
        }
    }  // namespace special
}  // namespace nc

#endif // #if defined(__cpp_lib_math_special_functions) || !defined(NUMCPP_NO_USE_BOOST)
